Hopefully, Orly will make an Appointments Clause challenge to get to the heart of the matter.
Officers Under the Appointments Clause, by John Plecnik
http://engagedscholarship.csuohio.edu/cgi/viewcontent.cgi?article=1783&context=fac_articles
All evidence of US law is held in trust by the Archivist of the United States. The Archivist is appointed by the President. An ineligible President invalidates appointments made pursuant to the Appointments Clause. Evidence of law held in trust by an Archivist appointed by an ineligible President put the Judiciary Act, as amended, in jeopardy.
The Judiciary Act provided authority for the District Court to operate. This Act established a circuit court and district court in each judicial district. An ineligible President voids the authority of the District Court and ultimately the U.S. Constitution. The courts are avoiding eligibility challenges to preserve the status quo with disregard for their oaths to support the U.S. Constitution.